Question

Can you help me answer part A and part B?

Answer 1

Part A.

Given:

P = (5, 4), Q = (7, 3), R = (8, 6), S = (4, 1)

Let's find the component of the vector PQ + 5RS.

To find the component of the vector, we have:

`=\lparen Q_1-P_1,Q_2-P_2)=<7-5,3-4>`

For vector RS, we have:

`=\lparen S_1-R_1,S_2-R_2)=<4-8,1-6>`

Hence, to find the vector PQ+5RS, we have:

`\begin{gathered} =<7-5,3-4>+5<4-8,1-6> \\ \\ =\left(2,-1\right)+5\left(-4,-5\right) \\ \\ =\left(2,-1\right)+\left(5\ast-4,5\ast-5\right) \\ \\ =\left(2,-1\right)+\left(-20,-25\right) \end{gathered}`

Solving further:

`\begin{gathered} =<2-20,-1-25> \\ \\ =<-18,-26> \end{gathered}`

Therefoee, the component of the vector PQ+5RS is:

<-18, -26>

• Part B.

Let's find the magnitude of the vector PQ+5RS.

To find the magnitude, apply the formula:

`m=√(\left(x^2+y^2\right?)`

Thus, we have:

`\begin{gathered} m=√(\left(-18^2+-26^2\right?) \\ \\ m=√(324+676) \\ \\ m=√(1000) \\ \\ m=√(10\ast10^2) \\ \\ m=10√(10) \end{gathered}`

Therefore, the magnitude of the vector is:

`10√(10)`

ANSWER:

Part A. <-18, -26>

Part B. 10√10